Jean-Luc Godard, who will soon celebrate his 84th birthday, holds a special place in the pantheon of modern cinema. He is an imp who is venerated as a deity, a Rorschach test, a lightning rod, a fighting word. His name seems to divide the world into skeptics and worshipers, with not much middle ground. Analogous figures can be found in other zones of 20th-century art: Andy Warhol, Bob Dylan, Ezra Pound. They have their singularity in common. They also tend to confound easy distinctions between genius and trickery, and to marshal armies of exegetes in what may be the futile enterprise of figuring out what they mean.

Mr. Godard has a habit of blending gravity with whimsy. His latest film, a 70-minute 3-D visual essay called “Goodbye to Language” (“Adieu au Langage”), exhibits the formal and philosophical mischief that has been his late-career calling card. It is baffling and beautiful, a flurry of musical and literary snippets arrayed in counterpoint to a series of brilliantly colored and hauntingly evocative pictures — of flowers, boats, streets, naked bodies and Mr. Godard’s own dog, a mixed-breed scene-stealer identified in the credits as Roxy Miéville.

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A scene from "Goodbye to Language," directed by Jean-Luc Godard.CreditKino Lorber

There is also the suggestion of a plot, or rather a gesture in the direction of a weave of narratives involving political intrigue and adultery and touching on some of the filmmaker’s recurrent preoccupations. These include the nightmares of the European, with special attention to imperialism and the Holocaust; the alienation of human emotion under capitalism; and the contradictory nature of cinema itself as both the repository and the destroyer of memory. “Goodbye to Language” is divided into chapters with the headings “Nature” and “Metaphor,” suggesting the basic division, fundamental to human thought, between the world we encounter and the names we assign to its phenomena.

In the 1960s, as Mr. Godard ascended to international culture-hero status, one of his most eloquent English-language champions was Susan Sontag. Nearly 50 years later, he may be returning the favor by making movies that uphold the arguments of her great essay “Against Interpretation,” which protested culture and criticism’s tireless and tiresome hunt for meaning.

“In place of a hermeneutics we need an erotics of art,” she concluded, and “Goodbye to Language” rewards just such an approach. If you try, especially on a first viewing, to crack its code or plumb its depths, you are likely to pass a frustrated hour and 10 minutes. But if you surrender, you might have a good time. The earth might even move.

Mr. Godard’s embrace of digital video — most notably in his 2001 film, “In Praise of Love” — helped to reveal that format’s latent aesthetic potency. He accomplishes something similar with 3-D in “Goodbye to Language.” There are none of the usual special effects to be seen here: Mr. Godard has no interest in capturing the magic of flight or making monsters seem real. Instead, the everyday world is made vivid and strange, rendered in a series of sketches and compositions by an artist with an eccentric and unerring eye.

He is delighted by paradoxes of flatness and depth, for example, the way the flat surface of a television showing an old-fashioned two-dimensional movie changes the volume of a room. He also, just for fun, superimposes one person on another, creating a jarring hallucination. At another point, he films a naked woman holding a platter on which a pitcher and a bowl of fruit have been arranged, combining two major genres of painting (the nude and the still life) into a moment of naturalistic surrealism.

It’s not all about pleasure, though. Much of the film is spent with a couple in a state of casual undress and post-coital ennui. She speaks in philosophical riddles and proverbs, the sources of which can be inferred from the cryptic bibliography that appears, along with a list of composers, in the end credits. He sits on the toilet, defecating loudly and opining that this action represents the only true form of human equality. “A position and a function” that we all share.

But it is worth noting that the man and the woman have, within the film, distinct functions and positions. Not only does she remain standing while he conducts his business, but her own business is also, in no small part, to be displayed as an object for contemplation and erotic reverie. He, too, is naked, but the camera is far more interested in looking at her.

An old cinematic god can hardly be expected to learn new tricks, and women’s bodies have often served Mr. Godard — and not only him, goodness knows — as convenient metaphors for the mysteries of nature and the forces that lie on the far side of language. That is, no doubt, a topic for further discussion. In any case this movie, its title notwithstanding, is unlikely to be the filmmaker’s last word.

Written, directed and edited by Jean-Luc Godard; director of photography, Fabrice Aragno; costumes by Aude Grivas; produced by Alain Sarde, Brahim Chioua and Vincent Maraval; released by Kino Lorber. In French, with English subtitles. Running time: 1 hour 10 minutes. This film is not rated.